The performance of advanced optical imaging or communication systems is often limited by the need to simultaneously select a small fractional frequency bandwidth and possess a large acceptance angle. For instance, the performance characteristics such as data rate and distance of optical communication systems that rely on laser beams propagating through turbulent media (submarine communication, ground to cloud communication) are dramatically enhanced by suitable bandwidths and acceptance angles. Such systems must have a narrow acceptance bandwidth in order to benefit from the intrinsically narrow linewidth of the laser and reject ambient light, while being able to handle laser beams reaching the detector from multiple directions due to scattering in the propagating medium. Small operating fractional linewidths of 10−3 to 10−7 coupled with a relatively large angular acceptance of plus or minus 10 to 30 degrees can enable radically improved system performance. Other applications include astronomical telescopes that image very narrow atomic/ionic emission lines of extended objects, where the desired angular field of view is substantial. This essential function of narrow spectral acceptance and wide angular acceptance is handled by specialty optical filters.
There are several technologies that attempt to fulfill optical filter requirements, but none meets them all simultaneously.
The most common method is based on planar structures that induce interference in order to sharpen the spectral response. The techniques may be based on Fabry-Perot cavities, solid etalons, multilayer dielectric stacks or other similar geometries. In all instances, the underlying phenomenon is the same, and its limitation has been widely understood: even small deviations from the designed angle of incidence cause the central frequency to shift out of the designed value by more than the nominal bandwidth. In fact, the bandwidth has a functional dependence on the acceptance angle α, which is proportional to (secα−1). At very small angles, the bandwidth behaves as the square of the angle, but the higher order terms in the series expansion of the sec function become dominant quite quickly. Consequently the bandwidth grows first quadratically with acceptance angle, then even more rapidly. This is a fundamental limitation on the acceptance angle of all narrow-bandwidth planar interference-based filters (see FIG. 1). Furthermore, the smaller the required fractional bandwidth the more complex the filter design, and the more lossy the filter. Multilayers comprising in excess of 200 layers may be required, and the unavoidable scattering losses at each of the interfaces can amount to significant transmission losses, in addition to the complex fabrication and dimensional control required of each layer (Reference 1).
A different principle is involved when the wavelength selectivity is obtained by utilizing birefringent crystals in conjunction with polarization selective filters (References 2-7). If several birefringent crystals are arranged with suitable orientation and crystal lengths, incident light at select frequencies is decomposed into two polarizations in such a way that when they recombine at the exit, they interfere with other destructively, except over a narrow bandwidth. Such birefringence-based filters come in several versions, known as Lyot filters, Lyot-Ohman filters, Solc filters, and so on. These filters have potentially a wider angular field of view than the equivalent Fabry-Perot filters, although the angle still depends on the bandwidth in a quadratic manner (Reference 2). The birefringent filters have their own limitations, mainly their bulkiness and the need to laboriously align the components (crystals, polarizers).
One specific kind of birefringence-based filter has been proposed, which can overcome the angle-bandwidth tradeoff (References 8, 9). However, it can be realized only when there is a crystal with unique properties, such that it has zero birefringence at the operating wavelength but non-zero birefringence at all other wavelengths. In other words, the two indices of refraction have independent wavelength-varying dispersion behavior in such a way that they “cross” at the operating wavelength; hence the term “zero crossing” filter. If such a crystal can be found, then the bandwidth is determined by the dispersion of the birefringence rather than by the birefringence itself, and it is independent of angle of incidence. In practice, only one such crystal has been proposed, cadmium sulfide (CdS), and even it does not have a true zero crossing, though at one specific wavelength it has a wide angle of acceptance (see FIG. 2). Furthermore, this wavelength is determined by the intrinsic crystal properties and cannot be adjusted.
A completely different approach employs very narrow-bandwidth transitions in select atoms, where the wavelength to be detected coincides with an atomic excitation transition, and the detection itself is carried out at a (usually longer) re-emission wavelength. The atoms are most commonly in gaseous phase and require suitable magnetic fields and temperature stabilization. Filters based on the Cs-atom transitions in the blue (˜455 nm) have been engineered (References 10, 11), and filters based on other alkali atoms (Reference 12) have been proposed or demonstrated in the laboratory. While these atomic filters have a very narrow bandwidth, as low as 0.001 nm, and angle of acceptance limited only by the overall system optics, they are also large, complex, cumbersome, and environmentally sensitive. The wavelengths at which they operate comprise a limited set with little tuning flexibility, as they are determined by the available atoms and their energy levels.